Optimal Dynamic Strings

Adam Karczmarz
Paweł Gawrychowski
Piotr Sankowski
Tomasz Kociumaka
SODA 2018 (to appear)
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In this paper we study the fundamental problem of maintaining a dynamic collection of strings under the following operations: (a) make_string -- add a string of constant length, (b) concatenate -- concatenate two strings, (c) split -- split a string into two at a given position, (d) compare -- find the lexicographical order (less, equal, greater) between two strings, (e) LCP -- calculate the longest common prefix of two strings. We develop a generic framework for dynamizing the recompression method recently introduced by Jeż [J. ACM 2016]. It allows us to present an efficient data structure for the above problem, where an update requires only O(log n) worst-case time with high probability, with n being the total length of all strings in the collection, and a query takes constant worst-case time. On the lower bound side, we prove that even if the only possible query is checking equality of two strings, either updates or queries must take amortized Omega(log n) time; hence our implementation is optimal.